Scalar-based strain gradient plasticity theory to model size-dependent kinematic hardening effects

A common belief in phenomenological strain gradient plasticity modeling is that including the gradient of scalar variables in the constitutive setting leads to size-dependent isotropic hardening, whereas the gradient of second-order tensors induces size-dependent kinematic hardening. The present paper shows that it is also possible to produce size-dependent kinematic hardening using scalar-based gradient theory. For this purpose, a new model involving the gradient of the equivalent plastic strain is developed and compared with two reference scalar-based and tensor-based theories. Theoretical investigations using simple monotonic loading conditions are first presented to assess the ability of the proposed model to solve some issues related to existing scalar-based gradient theories. Simulations under cyclic loading conditions are then provided to investigate the nature of the resulting hardening. These simulations show that the proposed model is capable of producing size-dependent kinematic hardening effects at more affordable costs, compared to existing tensor-based strain gradient plasticity theories

Congrès français de mécanique (21; 2013; Bordeaux (Gironde))

The indentation response of glasses can be classified into three classes : normal, anomalous and intermediate depending on the deformation mechanism and the cracking response. Silica glass, as a typical anomalous glass, deforms primarily by densification and has a strong tendency to form cone cracks that can accompany median, radial and lateral cracks when indented with a Vickers tip. This is due to its propensity to deform elastically by resisting plastic flow. Several investigations of this anomalous behavior can be found in the literature. The present paper serves to corroborate these results numerically using the discrete element method. A new pressure-densification model involving the discrete element method (DEM) is developed that allows for a quantitative estimate of the densification under very high pressure. This model is then used to simulate the Vickers indentation response of silica glass under various indentation forces. The numerical results obtained compare favorably with past experimental results

A multi-scale coupling method to simulate the silica glass behavior under high pressures

The response of glasses subjected to high pressures can be classified into three classes : normal, anomalous and intermediate depending on the deformation mechanism and the cracking pattern. The silica glass which is the scope of this work is a typical anomalous glass. The numerical study of this behavior with continuum methods (e.g. FEM, CNEM) presents several difficulties and drawbacks. Because, this requires a very small scale analysis. The discrete methods (e.g. MD, DEM) represent a good choice to simulate this behavior. However, these methods are very time consuming (CPU-wise). In this work, a discrete-continuum coupling method is proposed to study the behavior of this brittle material subjected to high pressures. The coupling results, obtained in this work, compare favorably with past experimental results

Uncoupled dissipation assumption to control elastic gaps in Gurtin-type strain gradient models

Thanks to their capabilities in capturing size effects, strain gradient plasticity theories have received a strong scientific interest in the last two decades. However, despite the great scientific effort on these theories, several challenging issues related to them remain to be addressed. One of these issues is concerned with the description of the dissipative processes due to plastic strains and plastic strain gradients. In almost all existing strain gradient works, such processes are described using generalized effective plastic strain measures, which imply plastic strains and their gradients in a coupled manner. This kind of (coupled) measures makes the issue of proposing robust and flexible dissipation formulations and the control of important dissipative effects difficult. Using such measures, it is not easy to control, for example, the elastic gaps at initial yield or under non-proportional loading. However, in most cases, the coupling between dissipative processes is only used by assumption. Its consistency with the current understanding of small scale plasticity is not confirmed in the literature. In spirit of multi-criterion approaches available in the literature, the present work proposes a flexible uncoupled dissipation assumption to describe dissipative processes. These processes are assumed to be derived from a pseudo-potential that is a sum of two independent functions of plastic strains and plastic strain gradients. Using this assumption, a new Gurtin-type strain gradient crystal plasticity (SGCP) model is developed and applied to simulate various two-dimensional plane-strain tests under proportional and non-proportional loading conditions. Results associated with these tests show the great flexibility of the proposed model in controlling some major dissipative effects, such as elastic gaps. A simple way to remove these gaps under certain non-proportional loading conditions is provided. Application of the proposed uncoupling assumption to simulate the mechanical response of a sheared strip has led to accurate prediction of the plastic strain distributions, which compare very favorably with those predicted using discrete dislocation mechanics

Strain Localization Modes within Single Crystals Using Finite Deformation Strain Gradient Crystal Plasticity

The present paper aims at providing a comprehensive investigation of the abilities and limitations of strain gradient crystal plasticity (SGCP) theories in capturing different kinds of localization modes in single crystals. To this end, the small deformation Gurtin-type SGCP model recently proposed by the authors, based on non-quadratic defect energy and the uncoupled dissipation assumption, is extended to finite deformation. The extended model is then applied to simulate several single crystal localization problems with different slip system configurations. These configurations are chosen in such a way as to obtain idealized slip and kink bands as well as general localization bands, i.e., with no particular orientation with respect to the initial crystallographic directions. The obtained results show the good abilities of the applied model in regularizing various kinds of localization bands, except for idealized slip bands. Finally, the model is applied to reproduce the complex localization behavior of single crystals undergoing single slip, where competition between kink and slip bands can take place. Both higher-order energetic and dissipative effects are considered in this investigation. For both effects, mesh-independent results are obtained, proving the good capabilities of SGCP theories in regularizing complex localization behaviors. The results associated with higher-order energetic effects are in close agreement with those obtained using a micromorphic crystal plasticity approach. Higher-order dissipative effects led to different results with dominant slip banding

On the non-quadratic defect energy in strain gradient crystal plasticity

Strain gradient crystal plasticity (SGCP) represents a very promising way to account for size effects in miniaturized components, thanks to the intrinsic length scale(s) embedded. Most of the existing SGCP models are based on a quadratic form of defect energy. However, it has recently been shown that this form leads to physically unrealistic results concerning the size-dependence of the mechanical response of miniaturized components. A generalized non-quadratic form is proposed in this work which aims to study the influence of the defect energy order on the global response of size-dependent materials

On the application of strain gradient crystal plasticity to study strain localization phenomena in single crystals

Strain localization is an important plastic instability process occurring prior to fracture. It is usually observed in the form of narrow bands of intense plastic shear strain in deformed bodies undergoing severe inhomogeneous deformation. Considering a single crystal with single slip system activated, two types of shear bands, known as slip and kink bands, may occur according to the seminal work of Asaro and Rice [1] based bifurcation analysis. Conventional crystal plasticity (CCP) theories have widely been applied in the literature to study strain localization within single crystals. Although these theories are able to capture several kinds of localization modes including slip and kink bands, they present mesh-dependence difficulties. In addition, CCP theories identically predict slip and kink bands which appear in this framework as equivalent bifurcation modes. Consequently, CCP theories are not suitable to study localization phenomena in single crystals. These theories include no internal length scale(s) allowing for stabilizing localization which theoretically will occur in a set of zero measure. A solution to overcome limitations of the aforementioned theories consists in applying nonlocal plasticity approaches. Including internal length scale(s), these approaches provide a natural framework to capture nonlocal effects. One class of nonlocal approaches, which presents auspicious features to capture localization phenomena in single crystals, is the class of strain gradient crystal plasticity (SGCP) theories. This class has been the subject of a large number of recent works mostly focusing on size effects [2, 3]. However, only a few works applying SGCP theories to study localization phenomena can be found in the literature. In almost all existing studies of localization phenomena in single crystals, only higher-order energetic effects have been considered. Higher-order dissipative effects on these phenomena have not yet been explored. Furthermore, there exist no works providing a comprehensive investigation of the abilities of SGCP theories in capturing different kinds of localization modes within single crystals, particularly the competition between slip and kind bands. The present contribution aims at tackling these tasks. To this end, a finite deformation SGCP model was developed and implemented within Abaqus/Standard using User-ELment (UEL) subroutine. This model was applied to simulate a uniaxial tension of a single crystal plate undergoing single slip. The objective of this simulation is to assess the effectiveness of the proposed model in capturing the complex localization behavior with competition between slip and kink bands

Simulation du comportement de la silice sous indentation Vickers par la méthode des éléments discrets: densification et mécanismes de fissuration

Le comportement mécanique des verres sous indentation microscopique est classiquement répertoriée en trois classes : normal, anormal ou intermédiaire selon les mécanismes de déformation et de fissuration. Particulièrement, la silice est un verre typique de la classe dite anormale. Une fois indenté par un indenteur de type Vickers, ce type de verre subit dans un premier temps une forte densification se traduisant par une diminution locale du volume pouvant atteindre 17.4% dans la zone indentée. Ensuite, une fissure conique peut se développer autour de l'empreinte d'indentation avant que d'autres fissures radiales, médianes et latérales apparaissent. Plusieurs chercheurs ont travaillé sur ce type de verre pour comprendre ce comportement dit anormal et plusieurs papiers ont été publiés sur le sujet. Concrètement, tous ces travaux s'accordent à dire que la principale cause de la déformation permanente (densification) de la silice est la pression hydrostatique. Ce travail concerne la mise en œuvre numérique par la méthode des éléments discrets de ce phénomène de densification. Un nouveau modèle spécifique de densification adapté à la méthode des éléments discrets a été développé. Après calibration et validation de ce modèle à l'échelle macroscopique, des simulations d'indentation microscopique avec un indenteur de type Vickers ont été réalisées. Confrontés à des résultats expérimentaux, les résultats numériques obtenus permettent une bonne estimation quantitative de l'état de densification et des mécanismes de fissuration

Discrete-continuum coupling method for simulation of laser-inducced damage in silica glass

A discrete-continuum coupling approach has been developed to simulate the laser-induced damage in silica glass. First, a classification of the different numerical methods has been performed to select the ones that best meet the objectives of this work. Acting upon this classification, the Discrete Element Method (DEM) and the Constrained Natural Element Method (CNEM) have been retained. Subsequently, a coupling approach between these methods has been proposed. This approach is based on the Arlequin technique. In the second part, a numerical model of the silica glass mechanical behavior has been developed to better characterize the silica glass response under highly dynamic loadings and particularly loading generated by a laser beam. To correctly characterize the silica glass cracking mechanisms, a new fracture model has been proposed in this work. Finally, all these developments have been used to simulate the laser-induced damage in silica glass.Une méthode de couplage continu-discret a été développée pour simuler les mécanismes complexes d'endommagement de la silice soumise à un choc laser de haute puissance. Dans un premier temps, une classification des méthodes numériques existantes a été faite pour choisir celles les mieux adaptées à la simulation du comportement sous choc de la silice. Comme résultat de cette classification, deux méthodes ont été retenues: la méthode des éléments discrets (DEM) et la méthode des éléments naturels contraints (CNEM). Ces méthodes sont alors couplées en se basant sur la technique dite "Arlequin". Puis, un modèle numérique permettant de tenir compte des différents phénomènes qui caractérise le comportement de la silice sous haute pression a été développé. Pour bien caractériser les mécanismes de fissuration de la silice à l’échelle microscopique, un nouveau modèle de rupture a été développé dans ce travail. Finalement, ces deux modèles, modèle de comportement et modèle de rupture, ont été intégrés dans la méthode du couplage pour simuler d'un point de vue mécanique le choc laser sur un échantillon en silice

Couplage modèles discrets - modèles continus pour la simulation d'endommagement induit par choc laser sur la silice

Une méthode de couplage continu-discret a été développée pour simuler les mécanismes complexes d'endommagement de la silice soumise à un choc laser de haute puissance. Dans un premier temps, une classification des méthodes numériques existantes a été faite pour choisir celles les mieux adaptées à la simulation du comportement sous choc de la silice. Comme résultat de cette classification, deux méthodes ont été retenues: la méthode des éléments discrets (DEM) et la méthode des éléments naturels contraints (CNEM). Ces méthodes sont alors couplées en se basant sur la technique dite "Arlequin". Puis, un modèle numérique permettant de tenir compte des différents phénomènes qui caractérise le comportement de la silice sous haute pression a été développé. Pour bien caractériser les mécanismes de fissuration de la silice à l’échelle microscopique, un nouveau modèle de rupture a été développé dans ce travail. Finalement, ces deux modèles, modèle de comportement et modèle de rupture, ont été intégrés dans la méthode du couplage pour simuler d'un point de vue mécanique le choc laser sur un échantillon en silice.A discrete-continuum coupling approach has been developed to simulate the laser-induced damage in silica glass. First, a classification of the different numerical methods has been performed to select the ones that best meet the objectives of this work. Acting upon this classification, the Discrete Element Method (DEM) and the Constrained Natural Element Method (CNEM) have been retained. Subsequently, a coupling approach between these methods has been proposed. This approach is based on the Arlequin technique. In the second part, a numerical model of the silica glass mechanical behavior has been developed to better characterize the silica glass response under highly dynamic loadings and particularly loading generated by a laser beam. To correctly characterize the silica glass cracking mechanisms, a new fracture model has been proposed in this work. Finally, all these developments have been used to simulate the laser-induced damage in silica glass